Answer
$\sin\theta$ = $ \frac{3}{5}$
$\cos\theta$ =$ \frac{4}{5}$
$\tan\theta$ =$ \frac{3}{4}$
Work Step by Step
Given $\theta$ is in standard position. Spotting a Point P on terminal side of $\theta$, in the given diagram-
We find point P (4, 3)
Now, we may apply Definition I to find required trigonometric functions-
We got $ x = 4, y = 3$
Therefore r= $\sqrt (x^{2} + y^{2})$
= $\sqrt (4^{2} + 3^{2})$
= $\sqrt (16 + 9)$
= $\sqrt (25)$ = 5
i.e. $ x = 4, y = 3,$ and $ r= 5$
Applying Definition I-
$\sin\theta$ =$ \frac{y}{r}$ = $ \frac{3}{5}$
$\cos\theta$ =$ \frac{x}{r}$ =$ \frac{4}{5}$
$\tan\theta$ =$ \frac{y}{x}$ =$ \frac{3}{4}$
